# -*- coding: utf-8 -*-
"""
This file is part of FElupe.
FElupe is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
FElupe is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with FElupe. If not, see <http://www.gnu.org/licenses/>.
"""
from ..math import right_cauchy_green_deformation as right_cauchy_green
from ..math import strain, strain_stretch_1d
[docs]
class EvaluateFieldContainer:
r"""Methods to evaluate the deformation gradient and strain measures of a field
container.
Parameters
----------
field : FieldContainer
A container for fields.
Examples
--------
.. pyvista-plot::
>>> import felupe as fem
>>>
>>> mesh = fem.Rectangle(n=4)
>>> region = fem.RegionQuad(mesh)
>>> field = fem.FieldContainer([fem.FieldPlaneStrain(region, dim=2)])
>>>
>>> evaluate = fem.field.EvaluateFieldContainer(field)
>>> F = evaluate.deformation_gradient()
>>>
>>> F.shape # (3, 3, nquadraturepoints, ncells)
(3, 3, 4, 9)
>>> F[..., 0, 0] # deformation gradient of first cell, first quadrature point
array([[1., 0., 0.],
[0., 1., 0.],
[0., 0., 1.]])
See Also
--------
felupe.FieldContainer : A container which holds one or multiple (mixed) fields.
"""
def __init__(self, field):
self.field = field
[docs]
def strain(self, fun=strain_stretch_1d, tensor=True, asvoigt=False, n=0, **kwargs):
r"""Return the Lagrangian strain tensor or its principal values.
.. math::
:label: lagrangian-strain-tensor
\boldsymbol{E} = \sum_\alpha f_\alpha \left( \lambda_\alpha \right)
\ \boldsymbol{N}_\alpha \otimes \boldsymbol{N}_\alpha
By default, the Seth-Hill strain-stretch relation with a strain exponent of
zero is used, see Eq. :eq:`seth-hill-strain-tensor`.
.. math::
:label: seth-hill-strain-tensor
\boldsymbol{E} = \sum_\alpha \frac{1}{k} \left( \lambda_\alpha^k - 1 \right)
\ \boldsymbol{N}_\alpha \otimes \boldsymbol{N}_\alpha
Parameters
----------
fun : callable, optional
A callable for the one-dimensional strain-stretch relation. Its Signature
must be ``lambda stretch, **kwargs: strain`` (default is the log. strain,
:func:`~felupe.math.strain_stretch_1d` with ``k=0``).
tensor : bool, optional
Assemble and return the strain tensor if True or return its principal values
only if False. Default is True.
asvoigt : bool, optional
Return the symmetric strain tensor in reduced vector storage (default is
False).
n : int, optional
The index of the displacement field (default is 0).
**kwargs : dict, optional
Optional keyword-arguments are passed to the 1d strain-stretch relation.
Returns
-------
ndarray of shape (N, N, ...) tensor, (N!, ...) asvoigt or (N, ...) princ. values
The strain tensor or its principal values.
See Also
-------
math.strain : Compute a Lagrangian strain tensor.
math.strain_stretch_1d : Compute the Seth-Hill strains.
"""
return strain(
self.field, fun=fun, tensor=tensor, asvoigt=asvoigt, n=0, **kwargs
)
[docs]
def log_strain(self, tensor=True, asvoigt=False, n=0):
r"""Return the logarithmic Lagrangian strain tensor or its principal values.
.. math::
:label: log-strain-tensor
\boldsymbol{E} = \sum_\alpha \ln(\lambda_\alpha) \
\boldsymbol{N}_\alpha \otimes \boldsymbol{N}_\alpha
Parameters
----------
tensor : bool, optional
Assemble and return the strain tensor if True or return its principal values
only if False. Default is True.
asvoigt : bool, optional
Return the symmetric strain tensor in reduced vector storage (default is
False).
n : int, optional
The index of the displacement field (default is 0).
Returns
-------
ndarray of shape (N, N, ...) tensor, (N!, ...) asvoigt or (N, ...) princ. values
The strain tensor or its principal values.
See Also
-------
math.strain_stretch_1d : Compute the Seth-Hill strains.
math.strain : Compute a Lagrangian strain tensor.
"""
return strain(self.field, tensor=tensor, asvoigt=asvoigt, k=0)
[docs]
def green_lagrange_strain(self, tensor=True, asvoigt=False, n=0):
r"""Return the Green-Lagrange Lagrangian strain tensor or its principal values.
.. math::
:label: seth-hill-strain-tensor
\boldsymbol{E} = \sum_\alpha \frac{1}{2} \left( \lambda_\alpha^2 - 1 \right)
\ \boldsymbol{N}_\alpha \otimes \boldsymbol{N}_\alpha
Parameters
----------
tensor : bool, optional
Assemble and return the strain tensor if True or return its principal values
only if False. Default is True.
asvoigt : bool, optional
Return the symmetric strain tensor in reduced vector storage (default is
False).
n : int, optional
The index of the displacement field (default is 0).
Returns
-------
ndarray of shape (N, N, ...) tensor, (N * (N + 1) / 2, ...) asvoigt or (N, ...) princ. values
The strain tensor or its principal values.
See Also
-------
math.strain : Compute a Lagrangian strain tensor.
math.strain_stretch_1d : Compute the Seth-Hill strains.
"""
return strain(self.field, tensor=tensor, asvoigt=asvoigt, k=2)
